There is known a forward error correction (FEC) scheme in which each packet has a relatively high redundancy for an error correction capability in a receive side. However, compared to an automatic repeat request (ARQ) scheme, error correction can be performed in the receive side, and there is no delay generated by a re-transmission request, so that the FEC scheme is suitable for a real-time data transmission system. Such an FEC scheme includes various techniques such as block coding, convolutional coding, turbo code (TC), and low density parity check (LPDC). FIG. 11 illustrates the FEC scheme having a 3/4 coding rate. It is recognized that 300 bits are redundant for each transmitted data of 900 bits, so that data are transmitted at a relatively high redundancy of approximately 33%.
In the case of the ARQ scheme such as a cyclic redundancy check (CRC), the redundancy of bits for detecting an error in a transmit signal is advantageously low. However, in the ARQ scheme, the error correction capability is not provided in the receive side, so that re-transmission is requested in the transmit side in the event of an error (no acknowledgement (NACK)). Therefore, compared to the FEC scheme having the error correction capability, the ARQ scheme is not suitable for a real-time service. FIG. 12 illustrates an exemplary ARQ scheme in which 31 bits for the CRC are transmitted, and re-transmission is requested in the event of “NACK.” Since redundant data of 31 bits are transmitted when a total of 1169 bits are transmitted, the data redundancy is low at approximately 3%.
Therefore, there are demands for development of an error detection and correction technology having both an error correction capability as in the FEC scheme and a low redundancy capability as in the ARQ scheme so as to implement less delay.
Meanwhile, a soft decision value represents a reliability as well as a bit value of “0” or “1” unlike a hard decision value. Assuming additive white Gaussian noise (AWGN), a receive signal yi (where i=1, 2, . . . ) can be expressed as follows:yi=xi+zi, i=1,2 . . . ,  [Equation 1]
where “xi” denotes a transmit signal (where i=1, 2 . . . ), and “zi” denotes a noise (where i=1, 2, . . . ) generated in the event of (i)th symbol transmission.
A soft decision value or a log likelihood ratio (LLR) can be obtained based on the aforementioned receive signal as follows:LLR(bk,i)=|yi−xi,k,−opt|2|−|yi−xi,k,+opt|2  [Equation 2]
where “bk,i” denotes the (k)th bit of the (i)th symbol (“k” is set to 1, 2, 3, and 4 in the case of 16-QAM), “xopti,k,−” denotes a point closest to “yi” out of constellation points having the (k)th bit set to “0,” and “xopti,k,+” denotes a point closest to “yi” out of constellation points having the (k)th bit set to “1.”
Assuming 16-QAM as illustrated in FIG. 13, the soft decision value of Equation 2 can be obtained as follows:
                              LLR          ⁡                      (                          b                              1                ,                i                                      )                          =                  {                                                                                                                                                                                                                            (                                                                                                y                                                                      I                                    ,                                    i                                                                                                  -                                                                  (                                  3                                  )                                                                                            )                                                        2                                                    -                                                                                    (                                                                                                y                                                                      I                                    ,                                    i                                                                                                  -                                                                  (                                                                      -                                    1                                                                    )                                                                                            )                                                        2                                                                          =                                                                                                            -                              8                                                        ⁢                                                                                                                  ⁢                                                          y                                                              I                                ,                                i                                                                                                              +                          8                                                                    ,                                                                                                  2                      <                                              y                                                  I                          ,                          i                                                                                                                                                                                                                                                                                            (                                                                                                y                                                                      I                                    ,                                    i                                                                                                  -                                                                  (                                  1                                  )                                                                                            )                                                        2                                                    -                                                                                    (                                                                                                y                                                                      I                                    ,                                    i                                                                                                  -                                                                  (                                                                      -                                    1                                                                    )                                                                                            )                                                        2                                                                          =                                                                              -                            4                                                    ⁢                                                                                                          ⁢                                                      y                                                          I                              ,                              i                                                                                                                          ,                                                                                                  0                      <                                              y                                                  I                          ,                          i                                                                    <                      2                                                                                                                                                                                                                                              (                                                                                                y                                                                      I                                    ,                                    i                                                                                                  -                                1                                                            )                                                        2                                                    -                                                                                    (                                                                                                y                                                                      I                                    ,                                    i                                                                                                  -                                                                  (                                                                      -                                    1                                                                    )                                                                                            )                                                        2                                                                          =                                                                              -                            4                                                    ⁢                                                                                                          ⁢                                                      y                                                          I                              ,                              i                                                                                                                          ,                                                                                                                          -                        2                                            <                                              y                                                  I                          ,                          i                                                                    <                      0                                                                                                                                                                                                                                              (                                                                                                y                                                                      I                                    ,                                    i                                                                                                  -                                1                                                            )                                                        2                                                    -                                                                                    (                                                                                                y                                                                      I                                    ,                                    i                                                                                                  -                                                                  (                                                                      -                                    3                                                                    )                                                                                            )                                                        2                                                                          =                                                                                                            -                              8                                                        ⁢                                                                                                                  ⁢                                                          y                                                              I                                ,                                i                                                                                                              -                          8                                                                    ,                                                                                                                          y                                                  I                          ,                          i                                                                    <                                              -                        2                                                                                                        ⁢                                                          ⁢                              LLR                ⁡                                  (                                      b                                          2                      ,                      i                                                        )                                                      =                          {                                                                                                                                                                                                                                                                        (                                                                                                            y                                                                              I                                        ,                                        i                                                                                                              -                                    3                                                                    )                                                                2                                                            -                                                                                                (                                                                                                            y                                                                              I                                        ,                                        i                                                                                                              -                                    1                                                                    )                                                                2                                                                                      =                                                                                                                            -                                  4                                                                ⁢                                                                                                                                  ⁢                                                                  y                                                                      I                                    ,                                    i                                                                                                                              +                              8                                                                                ,                                                                                                                      2                          <                                                      y                                                          I                              ,                              i                                                                                                                                                                                                                                                                                                                                                (                                                                                                            y                                                                              I                                        ,                                        i                                                                                                              -                                    3                                                                    )                                                                2                                                            -                                                                                                (                                                                                                            y                                                                              I                                        ,                                        i                                                                                                              -                                    1                                                                    )                                                                2                                                                                      =                                                                                                                            -                                  4                                                                ⁢                                                                                                                                  ⁢                                                                  y                                                                      I                                    ,                                    i                                                                                                                              +                              8                                                                                ,                                                                                                                      0                          <                                                      y                                                          I                              ,                              i                                                                                <                          2                                                                                                                                                                                                                                                                                          (                                                                                                            y                                                                              I                                        ,                                        i                                                                                                              -                                                                          (                                                                              -                                        3                                                                            )                                                                                                        )                                                                2                                                            -                                                                                                (                                                                                                            y                                                                              I                                        ,                                        i                                                                                                              -                                                                          (                                                                              -                                        1                                                                            )                                                                                                        )                                                                2                                                                                      =                                                                                          4                                ⁢                                                                                                                                  ⁢                                                                  y                                                                      I                                    ,                                    i                                                                                                                              +                              8                                                                                ,                                                                                                                                                  -                            2                                                    <                                                      y                                                          I                              ,                              i                                                                                <                          0                                                                                                                                                                                                                                                                                          (                                                                                                            y                                                                              I                                        ,                                        i                                                                                                              -                                                                          (                                                                              -                                        3                                                                            )                                                                                                        )                                                                2                                                            -                                                                                                (                                                                                                            y                                                                              I                                        ,                                        i                                                                                                              -                                                                          (                                                                              -                                        1                                                                            )                                                                                                        )                                                                2                                                                                      =                                                                                          4                                ⁢                                                                                                                                  ⁢                                                                  y                                                                      I                                    ,                                    i                                                                                                                              +                              8                                                                                ,                                                                                                                                                  y                                                          I                              ,                              i                                                                                <                                                      -                            2                                                                                                                                ⁢                                                                          ⁢                                      LLR                    ⁡                                          (                                              b                                                  3                          ,                          i                                                                    )                                                                      =                                  {                                                                                                                                                                                                                                                                                                                    (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                                                                  (                                                                                      -                                            1                                                                                    )                                                                                                                    )                                                                        2                                                                    -                                                                                                            (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                                                                  (                                          3                                          )                                                                                                                    )                                                                        2                                                                                                  =                                                                                                      8                                    ⁢                                                                                                                                                  ⁢                                                                          y                                                                              R                                        ,                                        i                                                                                                                                              -                                  8                                                                                            ,                                                                                                                                          2                              <                                                              y                                                                  R                                  ,                                  i                                                                                                                                                                                                                                                                                                                                                                                                    (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                                                                  (                                                                                      -                                            1                                                                                    )                                                                                                                    )                                                                        2                                                                    -                                                                                                            (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                                                                  (                                          1                                          )                                                                                                                    )                                                                        2                                                                                                  =                                                                  4                                  ⁢                                                                                                                                          ⁢                                                                      y                                                                          R                                      ,                                      i                                                                                                                                                                  ,                                                                                                                                          0                              <                                                              y                                                                  R                                  ,                                  i                                                                                            <                              2                                                                                                                                                                                                                                                                                                                                      (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                                                                  (                                                                                      -                                            1                                                                                    )                                                                                                                    )                                                                        2                                                                    -                                                                                                            (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                        1                                                                            )                                                                        2                                                                                                  =                                                                  4                                  ⁢                                                                                                                                          ⁢                                                                      y                                                                          R                                      ,                                      i                                                                                                                                                                  ,                                                                                                                                                                          -                                2                                                            <                                                              y                                                                  R                                  ,                                  i                                                                                            <                              0                                                                                                                                                                                                                                                                                                                                      (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                                                                  (                                                                                      -                                            3                                                                                    )                                                                                                                    )                                                                        2                                                                    -                                                                                                            (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                        1                                                                            )                                                                        2                                                                                                  =                                                                                                      8                                    ⁢                                                                                                                                                  ⁢                                                                          y                                                                              R                                        ,                                        i                                                                                                                                              +                                  8                                                                                            ,                                                                                                                                                                          y                                                                  R                                  ,                                  i                                                                                            <                                                              -                                2                                                                                                                                                        ⁢                                                                                          ⁢                                              LLR                        ⁡                                                  (                                                      b                                                          4                              ,                              i                                                                                )                                                                                      =                                          {                                                                                                                                                                                                                                                                              (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                        3                                                                            )                                                                        2                                                                    -                                                                                                            (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                        1                                                                            )                                                                        2                                                                                                  =                                                                                                                                            -                                      4                                                                        ⁢                                                                                                                                                  ⁢                                                                          y                                                                              R                                        ,                                        i                                                                                                                                              +                                  8                                                                                            ,                                                                                                                                          2                              <                                                              y                                                                  R                                  ,                                  i                                                                                                                                                                                                                                                                                                                                                                                                    (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                        3                                                                            )                                                                        2                                                                    -                                                                                                            (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                        1                                                                            )                                                                        2                                                                                                  =                                                                                                                                            -                                      4                                                                        ⁢                                                                                                                                                  ⁢                                                                          y                                                                              R                                        ,                                        i                                                                                                                                              +                                  8                                                                                            ,                                                                                                                                          0                              <                                                              y                                                                  R                                  ,                                  i                                                                                            <                              2                                                                                                                                                                                                                                                                                                                                      (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                                                                  (                                                                                      -                                            3                                                                                    )                                                                                                                    )                                                                        2                                                                    -                                                                                                            (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                                                                  (                                                                                      -                                            1                                                                                    )                                                                                                                    )                                                                        2                                                                                                  =                                                                                                      4                                    ⁢                                                                                                                                                  ⁢                                                                          y                                                                              R                                        ,                                        i                                                                                                                                              +                                  8                                                                                            ,                                                                                                                                                                          -                                2                                                            <                                                              y                                                                  R                                  ,                                  i                                                                                            <                              0                                                                                                                                                                                                                                                                                                                                      (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                                                                  (                                                                                      -                                            3                                                                                    )                                                                                                                    )                                                                        2                                                                    -                                                                                                            (                                                                                                                        y                                                                                      R                                            ,                                            i                                                                                                                          -                                                                                  (                                                                                      -                                            1                                                                                    )                                                                                                                    )                                                                        2                                                                                                  =                                                                                                      4                                    ⁢                                                                                                                                                  ⁢                                                                          y                                                                              R                                        ,                                        i                                                                                                                                              +                                  8                                                                                            ,                                                                                                                                                                          y                                                                  R                                  ,                                  i                                                                                            <                                                              -                                2                                                                                                                                                                                                                                                                [                  Equation          ⁢                                          ⁢          3                ]            